Coffee is one of the most consumed beverages in the world. This has two main consequences: a high level of competitiveness among the players operating in the sector and an increasing pressure from the supply chain on the environment. These two aspects have to be supported by scientific research to foster innovation and reduce the negative impact of the coffee market on the environment. In this paper, we describe a mathematical model for espresso coffee extraction that is able to predict the chemical characterisation of the coffee in the cup. Such a model has been tested through a wide campaign of chemical laboratory analyses on espresso coffee samples extracted under different conditions. The results of such laboratory analyses are compared with the simulation results obtained using the aforementioned model. The comparison shows a close agreement between the real and in silico extractions, revealing that the model is a very promising scientific tool to take on the challenges of the coffee market.

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We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly related to the computational cost of the multiplication between the coefficient matrix and the vectors computed by the solver at each iteration. We propose an efficient technique for the calculation of the product of the coefficient matrix and a generic vector. This computation is mainly based on the well-known spectral decomposition in spherical coordinates of the Green's function of the Laplacian operator. We also show the efficiency of the proposed method through numerical simulations.